SOLUTION: Page 433 number 67 Find all of the errors in the following solution to an equation. 7/x=8/x+3 +1 7(x+3)=8x+1 7x+3=8x -x=-3 x=3

Question 203371This question is from textbook
: Page 433 number 67 Find all of the errors in the following solution to an
equation. 7/x=8/x+3 +1
7(x+3)=8x+1
7x+3=8x
-x=-3
x=3 This question is from textbook

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
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A proper way to eliminate fractions is to multiply both sides of the equation by the Lowest Common Denominator. The LCD for this equation is: x(x+3).

Note the parentheses which have been placed around the left and right sides. This helps you "do the right thing" by using the distributive property on the right side of the equation.

On the left side the x's cancel. The (x+3)'s cancel in the first term on the right side. Nothing cancels (there's no fraction) in the second term on the right:

Using the Commutative Property to rearrange the order so it looks like what you are given:

As you can see. The left side and the first term on the right side are the same as in the second equation you were given. The difference is the last part of the right side. You were given that this was 1. This indicates that only the two fractions were multiplied by the LCD. This is incorrect. We must both sides of the equation by the LCD in order to eliminate the fractions!

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The error here is that the Distributive Property was not used (or was used incorrectly) to multiply 7(x+3). We should get 7x + 21, not 7x + 3.

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There are no errors here. If one subtracts 8x from both sides of the equation, subtracts 3 from both sides of the equation and then multiplies (or divides) both sides of the equation by -1 becomes . (Remember, because of the earlier errors, x=3 is not the correct solution to the equation.) However I would have just subtracted 7x from both sides. This would make the equation and I'd be done in one step.

A correct solution:

Multiply both sides by the LCD:

Simplify:

Subtract 7x and 21 from both sides:

Factor:

For this product to be zero one of the factors must be zero (Zero Product Property):
or
Solving each:
or
So there are two solutions to
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